### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Another (more refined) look at the Wilf-equivalances of length 4 patterns

Speaker: **Jonathan Bloom**, Rutgers University

Date: Thursday, February 12, 2015 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

In this talk we will settle two recent conjectures in the area of enumerative combinatorics. First, we answer a conjecture of B. Sagan by finding a multi-statistic preserving bijection between 1423-avoiding permutations and 2413-avoiding permutations. This new bijection also generalizes a classical result, in the area of pattern avoidance, due to Stankova. In the second part of the talk, we employ the techniques used to construct the aforementioned bijection to also prove a conjecture of E. Egge from 2011. In particular, we show that certain pattern classes are, surprisingly, counted by the large Schroder numbers.

See: http://www.math.rutgers.edu/~russell2/expmath/